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Phase-matched relativistic harmonic generation in plasmas is observed for the first time. Third-harmonic light is detected and discriminated spectrally and angularly from the harmonics generated from competing processes. Its angular pattern is a narrow forward-directed cone, which is consistent with phase matching of a high-order transverse mode in a plasma. The signal level is found to be on the same order of magnitude for a circularly polarized pump pulse as for a linearly polarized pump pulse.